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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>



<b>assume </b><a NAME="E1:18"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E3:18"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="funct_6.html#E1:18"><i><font color="Green">E12</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a>, <a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<b>hence </b><a NAME="E4:18"/>
(  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_5.html#K4">uncurry</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_5.html#K4">uncurry</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_5.html#K6">uncurry'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_5.html#K6">uncurry'</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funcop_1.html#K2">--&gt;</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> )
 <b>by </b><i><a class="txt" href="funct_6.html#E1:18"><i><font color="Green">E12</font></i></a>, <a class="ref" href="funct_6.html#T16" target="_self">Th16</a>, <a class="ref" href="funct_6.html#T17" target="_self">Th17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>


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